The enthalpy of hydration is the change in enthalpy when an ion is dissolved in water to infinite diluteness. Enthalpy is a thermodynamic term for the internal energy of a system plus the product of the pressure and the volume of the system. Enthalpy of hydration is always negative.
Solutions are homogeneous mixtures, meaning that the materials making up the mixture are distributed evenly. Dissolving is an interaction between the molecules of two different substances that results in a homogeneous mix. When another material is dissolved in water, it is called hydration.
Dissolving can either give off or absorb energy. When water is involved, energy is always given off, resulting in a negative change in enthalpy and a solution that is warmer than the original water. Infinite diluteness means that adding more water will not result in more changes in energy.